Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
Table of Notes
<
1 - 30
31 - 60
61 - 81
>
<
1 - 30
31 - 60
61 - 81
>
page
|<
<
(58)
of 197
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div263
"
type
="
section
"
level
="
1
"
n
="
188
">
<
p
>
<
s
xml:id
="
echoid-s1725
"
xml:space
="
preserve
">
<
pb
o
="
58
"
file
="
527.01.058
"
n
="
58
"
rhead
="
2 LIBER STATICÆ
"/>
& </
s
>
<
s
xml:id
="
echoid-s1726
"
xml:space
="
preserve
">I K R Q in N M, & </
s
>
<
s
xml:id
="
echoid-s1727
"
xml:space
="
preserve
">per conſequens idem centrum figuræ I K R H S F T
<
lb
/>
O E P G Q, è tribus parallelogrammis compoſitæ, erit in recta N D vel A D.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1728
"
xml:space
="
preserve
">Quemadmodum vero in dato triangulo tria quadrangula in-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.058-01
"
xlink:href
="
fig-527.01.058-01a
"
number
="
93
">
<
image
file
="
527.01.058-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.058-01
"/>
</
figure
>
ſcripta ſunt, ita infinita inſcribi poſlunt, & </
s
>
<
s
xml:id
="
echoid-s1729
"
xml:space
="
preserve
">inſcriptæ figuræ
<
lb
/>
gravitatis centrum nihilo minus, ob cauſas jam commemo-
<
lb
/>
ratas, in A D rectâ erit. </
s
>
<
s
xml:id
="
echoid-s1730
"
xml:space
="
preserve
">Verumenimvero quò plura quadran-
<
lb
/>
gula inſcribuntur, eo minor trianguli A B C ab inſcriptis
<
lb
/>
differentia fuerit. </
s
>
<
s
xml:id
="
echoid-s1731
"
xml:space
="
preserve
">Parallelis enim à latere A B per media ſe-
<
lb
/>
gmenta A N, N M, M L, L D. </
s
>
<
s
xml:id
="
echoid-s1732
"
xml:space
="
preserve
">ductis, differentia poſterio-
<
lb
/>
ris ſitus erit dimidium differentiæ prioris. </
s
>
<
s
xml:id
="
echoid-s1733
"
xml:space
="
preserve
">Quapropter infinita hujuſmodi
<
lb
/>
progreſſione, & </
s
>
<
s
xml:id
="
echoid-s1734
"
xml:space
="
preserve
">appropinquatione figura tandem invenietur, ut differentia in-
<
lb
/>
ter ipſam & </
s
>
<
s
xml:id
="
echoid-s1735
"
xml:space
="
preserve
">triangulum quovis plano, quantumvis minimo, minorſit. </
s
>
<
s
xml:id
="
echoid-s1736
"
xml:space
="
preserve
">Vnde
<
lb
/>
ſequitur, Si A D gravitatis diameter eſt, differentiã põderis ſegmenti A D C
<
lb
/>
à pondere ſegmenti A D B quovis plano, quantumvis minimo, minorem
<
lb
/>
eſſe. </
s
>
<
s
xml:id
="
echoid-s1737
"
xml:space
="
preserve
">Quare ſic argumentor.</
s
>
<
s
xml:id
="
echoid-s1738
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1739
"
xml:space
="
preserve
">A. </
s
>
<
s
xml:id
="
echoid-s1740
"
xml:space
="
preserve
">Inæqualibus ponderibus aliquod pondus inveniri poteſt, quod ipſorum diffe-
<
lb
/>
rentiâ ſit minus.</
s
>
<
s
xml:id
="
echoid-s1741
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1742
"
xml:space
="
preserve
">O. </
s
>
<
s
xml:id
="
echoid-s1743
"
xml:space
="
preserve
">Atqui hiſce ponderibus A D C, A D B nullum pondus inveniri poteſt,
<
lb
/>
quod differentia ipſorum ſit minus.</
s
>
<
s
xml:id
="
echoid-s1744
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s1745
"
xml:space
="
preserve
">O. </
s
>
<
s
xml:id
="
echoid-s1746
"
xml:space
="
preserve
">Ponder a igitur A D C, A D B non differunt.</
s
>
<
s
xml:id
="
echoid-s1747
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1748
"
xml:space
="
preserve
">Ideoq́ue A D gravitatis diameter eſt, in eaq́ue propterea etiam gravitatis
<
lb
/>
centrum trianguli A B C. </
s
>
<
s
xml:id
="
echoid-s1749
"
xml:space
="
preserve
">C*ONCLVSIO*. </
s
>
<
s
xml:id
="
echoid-s1750
"
xml:space
="
preserve
">Cujusq́ue trianguli gravitatis
<
lb
/>
centrum eſt in rectâ, ab angulo in medium oppoſiti lateris punctum ductâ,
<
lb
/>
quod demonſtrari oportuit.</
s
>
<
s
xml:id
="
echoid-s1751
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div265
"
type
="
section
"
level
="
1
"
n
="
189
">
<
head
xml:id
="
echoid-head202
"
xml:space
="
preserve
">1 PROBLEMA. 3 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1752
"
xml:space
="
preserve
">Dato triangulo, gravitatis centrum invenire.</
s
>
<
s
xml:id
="
echoid-s1753
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1754
"
xml:space
="
preserve
">D*ATVM*. </
s
>
<
s
xml:id
="
echoid-s1755
"
xml:space
="
preserve
">A B C triangulum eſto.</
s
>
<
s
xml:id
="
echoid-s1756
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1757
"
xml:space
="
preserve
">Q*VAESITVM*. </
s
>
<
s
xml:id
="
echoid-s1758
"
xml:space
="
preserve
">Centrum gravitatis inveniendum eſt.</
s
>
<
s
xml:id
="
echoid-s1759
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div266
"
type
="
section
"
level
="
1
"
n
="
190
">
<
head
xml:id
="
echoid-head203
"
xml:space
="
preserve
">PRAGMATIA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1760
"
xml:space
="
preserve
">Ab A in medium B C recta A D ducatur, conſimiliter à C in medium
<
lb
/>
A B recta C E: </
s
>
<
s
xml:id
="
echoid-s1761
"
xml:space
="
preserve
">Gravitatis centrum F eſſe dico.</
s
>
<
s
xml:id
="
echoid-s1762
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div267
"
type
="
section
"
level
="
1
"
n
="
191
">
<
head
xml:id
="
echoid-head204
"
xml:space
="
preserve
">DEMONSTRATIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1763
"
xml:space
="
preserve
">Gravitatis centrum trianguli A B C eſt in re-
<
lb
/>
<
figure
xlink:label
="
fig-527.01.058-02
"
xlink:href
="
fig-527.01.058-02a
"
number
="
94
">
<
image
file
="
527.01.058-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.058-02
"/>
</
figure
>
ctis A D & </
s
>
<
s
xml:id
="
echoid-s1764
"
xml:space
="
preserve
">C E per 2 propoſ. </
s
>
<
s
xml:id
="
echoid-s1765
"
xml:space
="
preserve
">quod demonſtran-
<
lb
/>
dum fuit.</
s
>
<
s
xml:id
="
echoid-s1766
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1767
"
xml:space
="
preserve
">C*ONCLVSIO*. </
s
>
<
s
xml:id
="
echoid-s1768
"
xml:space
="
preserve
">Dato igitur triangulo, gravi-
<
lb
/>
tatis centrum invenimus, quod quærebatur.</
s
>
<
s
xml:id
="
echoid-s1769
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div269
"
type
="
section
"
level
="
1
"
n
="
192
">
<
head
xml:id
="
echoid-head205
"
xml:space
="
preserve
">3 THEOREMA. 4 PROPOSITIO.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1770
"
xml:space
="
preserve
">Centrum gravitatis cujusq́ue trianguli, rectam ab an-
<
lb
/>
gulo in oppoſitum latus medium ita ſecat: </
s
>
<
s
xml:id
="
echoid-s1771
"
xml:space
="
preserve
">ut ſegmentum
<
lb
/>
interipſum & </
s
>
<
s
xml:id
="
echoid-s1772
"
xml:space
="
preserve
">angulum, duplum ſit reliqui.</
s
>
<
s
xml:id
="
echoid-s1773
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>